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Many challenging engineering problems are regular, meaning solutions to one part of a problem can be reused to solve other parts. Evolutionary algorithms with indirect encoding perform better on regular problems because they reuse genomic information to create regular phenotypes. However, on problems that are mostly regular, but contain some irregularities, which describes most real-world problems, indirect encodings struggle to handle the irregularities, hurting performance. Direct encodings are better at producing irregular phenotypes, but cannot exploit regularity. An algorithm called HybrID combines the best of both: it first evolves with indirect encoding to exploit problem regularity, then switches to direct encoding to handle problem irregularity. While HybrID has been shown to outperform both indirect and direct encoding, its initial implementation required the manual specification of when to switch from indirect to direct encoding. In this paper, we test two new methods to improve HybrID by eliminating the need to manually specify this parameter. Auto-Switch-HybrID automatically switches from indirect to direct encoding when fitness stagnates. Offset-HybrID simultaneously evolves an indirect encoding with directly encoded offsets, eliminating the need to switch. We compare the original HybrID to these alternatives on three different problems with adjustable regularity. The results show that both Auto-Switch-HybrID and Offset-HybrID outperform the original HybrID on different types of problems, and thus offer more tools for researchers to solve challenging problems. The Offset-HybrID algorithm is particularly interesting because it suggests a path forward for automatically and simultaneously combining the best traits of indirect and direct encoding. [ABSTRACT FROM AUTHOR]